The present invention relates generally to signal processing systems, and more particularly to processing the step-like output signals generated by devices with multiple poles and zeros (including non-ideal, nominally single-pole (“N-1P”) devices as a subset) responding to possibly time-varying, pulse-like input signals of finite duration, wherein the goal is to recover the integrated areas of the input signals.
The specific embodiments described relate to processing step-like signals generated by detector systems in response to absorbed radiation or particles and, more particularly, to digitally processing such step-like signals in high resolution, high rate gamma ray (γ-ray) spectrometers with resistive feedback preamplifiers connected to large volume germanium detectors. The method also works well with gas proportional counters and scintillation detectors, to cite additional examples. The application of measuring the step-like output signals from γ-ray detector preamplifiers to measure the γ-rays' energies is given specific attention only because this was the area in which the method was first developed.
The techniques that we have developed solve this problem generally, and therefore should not be construed as being limited to this specific application. Any detection system, for example, that produces output current signals that are integrated by charge sensitive preamplifiers could be treated by these techniques, whether the detected quantities are light pulses, x-rays, nuclear particles, chemical reactions, or otherwise. The techniques, in fact, is not limited to “detector systems” per se, but are, in fact, general purpose signal processing techniques which may be broadly applied, once understood, to any device whose output signals that can be described in terms of multiple poles and zeros. The outputs from superconducting bolometers, for example, produce step-like signals that are readily treated by the invention, as do the outputs of photomultiplier tubes (PMTs) attached to scintillators having more than one decay time. The field of gamma spectroscopy, where 0.1% or less makes the difference between a bad and a good detector, however, provides particularly stringent tests of our techniques.
The term “step-like signal” also requires some discussion. The output of an ideal single-pole (“1-P ”) device to an ideal impulse (delta) function input, is an infinitely fast rise time followed by an exponential decay whose time constant τd is characteristic of the pole. Viewed on a time scale short compared to τd, this output will look like a pure step, while, when viewed on a time scale long compared to τd, it will look like a pulse. A real 1-P device output, however, will have a finite risetime, τr, whose duration will be determined both by the nature of the device and, particularly, by the duration of its real input signal. Provided that τr is significantly shorter than τd, a real 1-P device output signal, viewed on a time scale comparable to τd, will then show a risetime region, whose shape may be difficult to describe mathematically, followed, after a period comparable to τr, by an exponential decay with time constant τd. The output of a device with multiple poles will be similar, except that the decay will be described by multiple time constants τi, where I=1 for the first pole, 2 for the second, etc. The output of a N-1P device will also be similar, with additional distortions from added minor pole or zero terms. We will refer to such signals, viewed on this time scale, as “step-like” or “step-like pulses.” A pulse displaying step-like nature is shown in FIG. 1B.
Gamma-Ray (γ-Ray) Detection Requirements
The detection and measurement of γ-ray energies is a well-established discipline whose primary goal is to accurately determine both the number and energies of γ-rays emitted from some target source. The requirements of good energy resolution and high count rate capability usually conflict, however, since count rates are enhanced by increasing detector volume, which increases output signal distortion and so degrades energy resolution. High count rates also degrade energy resolution directly due to practical problems in preamplifier design.
Description of the Problems
The field of γ-ray detection is highly developed. A fairly comprehensive introduction to the state of the art may be found in the volume “Radiation Detection and Measurement, 2nd Ed.” by Glenn F. Knoll [KNOLL-1989]. Below we note only the issues relevant to the present invention. In the first section, we discuss how pole/zero cancellation errors introduce a second pole, spoiling the preamplifier's single pole response. In the second section, we examine how the finite input signal duration, in this case due to charge collection, distorts the preamplifier's output from the ideal.
Pole/Zero Cancellation Errors
FIG. 1A shows a typical solid state γ-ray spectrometer comprising a semiconductor detector diode 7 biased by a voltage supply 8 and connected to a preamplifier 10 comprising an amplifier 13 with a feedback capacitor C 15 and resistor R 17. As drawn, preamplifier 10 is a single pole circuit whose response to an impulse (delta function) input is A exp(−t/τ2), where τ2=RC and A is the area under the impulse. Because τ2 is typically of order 1 ms, which is too long for the following circuits, a pole/zero (P/Z) network 20 cancels the pole at 1/τ2 and replaces it with a pole at 1/τ1, where τ1 typically is 50 μs. Gain stage 22 then amplifies and buffers the preamplifier's output signal for shaping amplifier 23 which feeds multichannel analyzer (MCA) 24.
If the time duration of the current pulse arising from the charge deposited in detector 7 by a γ-ray absorption is very short compared to τ1, the output of stage 22 will be an exponentially decaying step whose amplitude is the pulse integral and proportional to the deposited charge. γ-ray spectrometers are therefore designed to measure these step amplitudes to measure the charge deposited by the absorbed γ-ray. Other forms of radiation, including neutrons, alpha and beta particles, and x-rays behave similarly and their energies are measured the same way.
Commonly, however, both the input's finite duration and the pole-zero circuit's imperfections distort the preamplifier's response, destroying the proportionality between the output step's amplitude and the deposited charge and so degrading the system's energy resolution. Imperfections in P/Z network 20 arise from difficulties in precisely canceling the τ2 component, leaving a small residual fraction, of order 1–2%, in the output signal. FIG. 1B shows a 5% residual τ2 component for ease of viewing: an exponential decay signal 25 with time constant τ2, input to the P/Z network 20, produces either output signal 27 or 29, depending upon whether the residual τ2 term is positive or negative.
These τ2 residuals are particularly bothersome at high counting rates, where each signal step rides upon a τ2 background from all preceding steps. As these arrive randomly, the resulting baseline bias also fluctuates randomly in time, which the spectroscopy amplifier's baseline restoration circuit cannot track well. These terms, which may only be a few tenths of 1%, become a significant resolution degradation at 1 MeV where 0.05% energy resolution is desired.
Signal Risetime Fluctuations and Ballistic Deficit
FIG. 2 shows a preamplifier 10 front end with a cross sectional view of the detector 7 of FIG. 1, for the common coaxial geometry, The dashed lines show electric field line within the detector body 30, which vary considerably with local geometry. Two factors cause charge collection time variations within the detector and thus risetime variations in the preamplifier's 10 signal output: 1) the difference between carrier velocities; and 2) the existence of different path lengths within the detector. RAUDORPH-1982 describes these issues. These risetime variations produce ballistic deficit by two paths, one direct, one indirect. The direct effect is well understood, per GOULDING-1988: the output filter's response varies with the time dependent shape of the charge arrival, being the convolution of the two. A trapezoidal filter greatly reduces this effect in the absence of exponential decay.
The indirect effect source of ballistic deficit is due to fluctuations in charge loss through the feedback resistor with differing risetime, as seen in FIG. 3A with two risetimes, 40 and 42, where FIG. 3B enlarges their peak regions. The slower risetime signal loses less charge and thus is larger once charge collection is complete. Even filters which ignore the charge collection region are still sensitive to this lost charge effect, and relatively small errors of this size can substantially degrade resolution. For a trapezoidal filter, the collection time difference shown FIG. 3B produces a 0.2% amplitude difference (2,000 eV at 1 MeV) which will degrade ideal 1.7 keV resolution to 2.6 keV. Ballistic deficit errors must therefore be reduced to less than 0.05% to obtain ideal spectrometer resolutions at 1 MeV.
Charge Trapping Losses
Charge trapping also produces errors in γ-ray energy measurements since trapped charges are lost to the measurement. The present invention does not seek to address this problem.
Scintillators with Multiple Decay Times
Scintillators generally convert the energy deposited in them by a photon or particle into a population of excited states that then decay, emitting light as they do so. The total light emitted may then be taken as a measure of the energy deposited. Light output from a scintillator is therefore also “step-like” in the sense we are discussing. In addition, certain scintillators possess more than one type of excited state, so that their decay is characterized by multiple decay times. CsI(T1), for example, has two decay times of about 600 ns and 4 μs, so that its output signals formally resemble trace 27 in FIG. 1B (the real time scale is about a factor of 100 faster, of course).
Generalizations
It is important to note that the pole-zero cancellation errors described above do not arise from the preamplifier's use in γ-ray spectroscopy, but are a generic problem in low noise, charge sensitive preamplifiers. Similarly, while the described risetime fluctuations described above were attributed to the geometry and construction of large volume Ge detectors, it is clear that such problems fundamentally arise from interactions between the finite charge collection time and the electrical characteristics of the preamplifier and not from the physics of the collection processes. Geometric heat flow variations in the photon absorbing mass produce similar effects in the superconducting bolometers mentioned earlier. Risetime issues are therefore a potentially general problem as well, and may need to be corrected for in other, non-γ-ray, detectors whenever the highest measurement accuracies are required. The methods we describe offer just that capability. Further, the terminology “single-pole” or “multiple-poles or zeros” comes from the LaPlace Transform treatment of differential equations describing time variant phenomena. Any device which shows “single-pole” behavior, for example, will display exponential time decay in response to an impulse input and, therefore, may be, for example, mechanical, thermal, chemical, or magnetic in nature in addition to the electronic case presented here. Our method can be directly applied to these devices as well, as will be apparent from the teachings herein.
Existing Correction Schemes
The prior art deals with pole/zero errors in two ways: first, by canceling τ2 as accurately as possible; and, second, with baseline restoration schemes which try to track the shaping amplifier's “no signal” output as closely as possible, an approach which degrades as rates becomes high. We have not found any approaches which measure and/or correct for the effect directly.
Over the years, various heuristic schemes have been developed which attempt to compensate for ballistic deficit. RADEKA-1982 introduced trapezoidal filtering and developed a time-variant implementation, using a gated filter following a semi-Gaussian shaper, that provided significant resolution improvements. WHITE-1988 proposed a different gated integration approach using a series switch to excise the charge collection region out of the preamplifier signal entirely. The final circuit was complex and had enhanced deadtime problems. GOULDING-1988, RAUDORF-1982, and SIMPSON-1990 disclose schemes that depend on directly measuring the signal's risetime tr and correcting the energy filter output by a term like trn. These approaches are complex to implement and require precise expert adjustments to operate. The underlying assumptions are not particularly valid and improvements in energy resolution have been modest in practice.
HINSHAW-1991 and KUMAZAWA-1998 describe attempts to correct for ballistic deficit by capturing peak amplitudes from two filters which respond to the ballistic deficit differently, one an energy measuring filter and one a differentiating (or bipolar shaping) filter. Typically a significant fraction of their difference in peak heights is added to the energy filter's peak to correct it.
Related Art
There is some related art wherein the details of the shapes of the preamplifier output signals are sampled digitally and used either to distinguish between different types of particles absorbed in the detector (e.g., MILLER-1994) or to distinguish between single and multiple interaction events in large germanium detectors. See, for example, TAKAHASHI-1994 and AALSETH-1998.
WARBURTON-1997, WARBURTON-1998, and WARBURTON-1999 describe methods for implementing digital filtering and x-ray spectroscopy. While they do not address the issues under consideration, some of their filtering techniques will be employed in the present invention and are referenced in the specification.